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Theory of Machines Miscellaneous

  1. A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed ω2. Length of different links are
    O2O4 = O2 A = L,
    AB = O4 B = 2 L
    The magnitude of the angular speed of the output link 4 is ω4 at the instant when link 2 makes an angle of 90° with O2O4 as shown. The ratio
    ω4
    is
    ω2

    _____ (round off to two decimal places).
    1. 0.79
    2. 0.88
    3. 0.25
    4. 0.99
Correct Option: A



Now, O4C = cos 75°
O4C = sin 75°
∆AO2I24 ≈ ∆BI24C

L
=
2Lsin75°
xx + L + √2cos75°


L
= 0.2679
x

ω4
=
1
= 0.7887 ≈ 0.79
ω21 + 0.267



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